Now, networks fall into the category of simplicial complexes, a kind of purely combinatorial objects whose homology can thus be computed combinatorically – i.e. with a computer. Hence, networks are all set for a homological study. However, we still need a way to assign an appearance time to the elements of a network if we want to use the tools of persistent homology. For weighted networks one can use the weights for this purpose [1]}, but unweighted networks require the extra step of deciding an appropriate time filtration. The triangle-augmented Forman-Ricci curvature has been proposed as a way of doing so [2]}, with the idea of having relevant edges (at least curvature-wise, i.e. with very negative curvature) appearing soon in the filtration, thus having key structural features of the network manifesting early in the process.
